# Poisson Confidence Interval

Menu location: **Analysis_Parametric_Poisson Confidence Interval**.

This function enables you to construct a confidence interval from a sample of observations drawn at random from a Poisson distribution.

Note that the Analysis_Distributions_Poisson menu item also provides Poisson confidence intervals for single counts. The function described in this section provides Poisson confidence intervals for series of counts.

The Poisson mean is estimated here as the arithmetic mean of the sample and the confidence interval is estimated using the relationship between the chi-square and Poisson distributions (Stuart and Ord, 1994; Johnson and Kotz, 1969):

- where χ^{2}_{α,ν} is the chi-square deviate with lower tail area α on ν degrees of freedom, n is the sample size and the sample mean is the point estimate of the Poisson parameter around which Y_{l} and Y_{u} are the lower and upper confidence limits respectively.

__Example__

Test workbook (Parametric worksheet: Reception).

Consider the following numbers from a hypothetical time and motion study in a hospital outpatients department. The numbers represent the number of patients arriving at the reception desk at five minute intervals during the mid-afternoon:

2, 1, 1, 0, 2, 1, 0, 2, 3, 1, 0, 1, 2, 2, 1, 0, 0, 1, 1, 2, 2, 1, 1

In order to analyse these data in StatsDirect you should enter them into a workbook and then select Poisson Confidence Interval from the Parametric section of the Analysis menu. You have the opportunity to specify a one or two sided interval.

For this example:

__Poisson Estimates__

Poisson analysis for Reception:

n = 23, mean = 1.173913

Approximate two sided 95% CI = 0.773616 to 1.707982